Given $ m \angle BOC = 3x + 90$, and $ m \angle AOB = 6x + 45$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 45} + {3x + 90} = {180}$ Combine like terms: $ 9x + 135 = 180$ Subtract $135$ from both sides: $ 9x = 45$ Divide both sides by $9$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 3({5}) + 90$ Simplify: $ {m\angle BOC = 15 + 90}$ So ${m\angle BOC = 105}$.